The detailed orbital-decomposed electronic structures of tetragonal ZrO2

The detailed orbital-decomposed electronic structures of the tetragonal zirconia have been investigated by using the first-principles projector augmented wave (PAW) potential within the generalized gradient approximation (GGA) as well as taking into account the on-site Coulomb repulsive interaction (GGA+U). The deviation of the minimization energy from dz=0 to dz=±0.032 for experimental lattice constants (a=3.605 Å and c=5.180 Å) confirms the alternating displacement of the oxygen atoms, which causes half of the Zr---O bonds stronger and the other half weaker compared with the bonds in symmetric (dz=0) zirconia. The distorted tetragonal environment of the eight oxygen anions around Zr site splits the five-fold degenerate d states of a free Zr atom into triply degenerate t2g (dxy, dyz and dzx) states and doubly degenerate eg (dz2 and dx2-y2) states. The additional covalent character upon Zr-O ionic bonds are resulted from the hybridization between the O(2s), O(2p) and Zr(5s), triply degenerate t2g (dxy, dyz and dzx) states of Zr(4d). The O(2s) and O(2p) states are clearly separated and no hybrid bonding states are formed